Direct approach-based analysis of plates composed of functionally graded materials

• DOI: 10.1007/s00419-007-0192-3
• Publication Date: 2007-12-21T13:40:18Z
• Authors: Holm Altenbach; Victor A. Eremeyev
• Keywords: Direct approach; Effective stiffness; Functionally graded materials; Plate theories; Transverse shear stiffness; 0203 mechanical engineering; 02 engineering and technology; [SPI.MECA] Engineering Sciences [physics]/Mechanics [physics.med-ph]; 0210 nano-technology

The classical plate theory can be applied to thin plates made of classical materials like steel. The first theory allowing the analysis of such plates was elaborated by Kirchhoff. But this approach was connected with various limitations (e.g., constant material properties in the thickness direction). In addition, some mathematical inconsistencies like the order of the governing equation and the number of boundary conditions exist. During the last century many suggestions for improvements of the classical plate theory were made. The engineering direction of improvements was ruled by applications (e.g., the use of laminates or sandwiches as the plate material), and so new hypotheses for the derivation of the governing equations were introduced. In addition, some mathematical approaches like power series expansions or asymptotic integration techniques were applied. A conceptional different direction is connected with the direct approach in the plate theory. This paper presents the extension of Zhilin's direct approach to plates made of functionally graded materials.